相关论文: Some divergent trigonometric integrals
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them.…
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral formula for divided differences. As part of the derivation we…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
We give several examples of tilting-discrete symmetric algebras; in particular, one explores which algebra has tilting-discrete trivial extension. We provide a counter example of the conjecture stating any {\tau} -tilting finite symmetric…
The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivial if and only if the knot is trivial. We will use…
We consider a rational-trigonometric deformation in context of rational and trigonometric deformations. The simplest examples of these deformations are presented in different fields of mathematics. Rational-trigonometric differential…
A descent of a labeled acyclic digraph is a directed edge $x\to y$ with $x>y$. In this paper, we find a recurrence for the number of labeled acyclic digraphs with a given number of descents.
Some inequalities for different types of convexity are established.
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
We prove that any derived equivalence between triangular algebras is standard, that is, it is isomorphic to the derived tensor functor given by a two-sided tilting complex.
Symmetry properties are at the basis of integrability. In recent years, it appeared that so called "twisted symmetries" are as effective as standard symmetries in many respects (integrating ODEs, finding special solutions to PDEs). Here we…
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…
Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…
An analogue of Taylor's formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results…
We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real…
We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…
It is shown that with appropriate boundary conditions, a real function satisfying the differential equation $f'(x) = f(x+a)$ has all known properties of the sine function. A number of elementary derivations are presented including proofs…
The combinatorics of tilings of a hexagon of integer side-length $n$ by 120 degree - 60 degree diamonds of side-length 1 has a long history, both directly (as a problem of interest in thermodynamic models) and indirectly (through the…